Complete Axiomatization for the Bisimilarity Distance on Markov Chains

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

2 Citations (Scopus)

Abstract

In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS'16) that uses equality relations t =_e s indexed by rationals, expressing that "t is approximately equal to s up to an error e". Notably, our quantitative deductive system extends in a natural way the equational system for probabilistic bisimilarity given by Stark and Smolka by introducing an axiom for dealing with the Kantorovich distance between probability distributions.
Original languageEnglish
Title of host publication27th International Conference on Concurrency Theory (CONCUR 2016)
Number of pages14
PublisherSchloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH
Publication date2016
Pages21:1--21:14
ISBN (Print)978-3-95977-017-0
DOIs
Publication statusPublished - 2016
Event27th International Conference on Concurrency Theory - Université Laval, Québec City, Canada
Duration: 23 Aug 201626 Aug 2016
Conference number: 27
http://www.concur2016.ulaval.ca/no_cache/home/

Conference

Conference27th International Conference on Concurrency Theory
Number27
LocationUniversité Laval
CountryCanada
CityQuébec City
Period23/08/201626/08/2016
Internet address
SeriesLeibniz International Proceedings in Informatics
Volume59
ISSN1868-8969

Fingerprint

Axiomatization
Markov chain
Equational Logic
Deductive System
Approximately equal
Axiom
Equality
Probability Distribution
Class
Style

Keywords

  • Markov chains
  • Behavioral Distances
  • Axiomatization

Cite this

Bacci, G., Bacci, G., Larsen, K. G., & Mardare, R. I. (2016). Complete Axiomatization for the Bisimilarity Distance on Markov Chains. In 27th International Conference on Concurrency Theory (CONCUR 2016) (pp. 21:1--21:14). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH. Leibniz International Proceedings in Informatics, Vol.. 59 https://doi.org/10.4230/LIPIcs.CONCUR.2016.21
Bacci, Giorgio ; Bacci, Giovanni ; Larsen, Kim Guldstrand ; Mardare, Radu Iulian. / Complete Axiomatization for the Bisimilarity Distance on Markov Chains. 27th International Conference on Concurrency Theory (CONCUR 2016). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, 2016. pp. 21:1--21:14 (Leibniz International Proceedings in Informatics, Vol. 59).
@inproceedings{c42ef849171d4944aa9a9b9d72509e45,
title = "Complete Axiomatization for the Bisimilarity Distance on Markov Chains",
abstract = "In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS'16) that uses equality relations t =_e s indexed by rationals, expressing that {"}t is approximately equal to s up to an error e{"}. Notably, our quantitative deductive system extends in a natural way the equational system for probabilistic bisimilarity given by Stark and Smolka by introducing an axiom for dealing with the Kantorovich distance between probability distributions.",
keywords = "Markov chains, Behavioral Distances, Axiomatization",
author = "Giorgio Bacci and Giovanni Bacci and Larsen, {Kim Guldstrand} and Mardare, {Radu Iulian}",
year = "2016",
doi = "10.4230/LIPIcs.CONCUR.2016.21",
language = "English",
isbn = "978-3-95977-017-0",
series = "Leibniz International Proceedings in Informatics",
publisher = "Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH",
pages = "21:1----21:14",
booktitle = "27th International Conference on Concurrency Theory (CONCUR 2016)",

}

Bacci, G, Bacci, G, Larsen, KG & Mardare, RI 2016, Complete Axiomatization for the Bisimilarity Distance on Markov Chains. in 27th International Conference on Concurrency Theory (CONCUR 2016). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Leibniz International Proceedings in Informatics, vol. 59, pp. 21:1--21:14, 27th International Conference on Concurrency Theory, Québec City, Canada, 23/08/2016. https://doi.org/10.4230/LIPIcs.CONCUR.2016.21

Complete Axiomatization for the Bisimilarity Distance on Markov Chains. / Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim Guldstrand; Mardare, Radu Iulian.

27th International Conference on Concurrency Theory (CONCUR 2016). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, 2016. p. 21:1--21:14 (Leibniz International Proceedings in Informatics, Vol. 59).

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

TY - GEN

T1 - Complete Axiomatization for the Bisimilarity Distance on Markov Chains

AU - Bacci, Giorgio

AU - Bacci, Giovanni

AU - Larsen, Kim Guldstrand

AU - Mardare, Radu Iulian

PY - 2016

Y1 - 2016

N2 - In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS'16) that uses equality relations t =_e s indexed by rationals, expressing that "t is approximately equal to s up to an error e". Notably, our quantitative deductive system extends in a natural way the equational system for probabilistic bisimilarity given by Stark and Smolka by introducing an axiom for dealing with the Kantorovich distance between probability distributions.

AB - In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS'16) that uses equality relations t =_e s indexed by rationals, expressing that "t is approximately equal to s up to an error e". Notably, our quantitative deductive system extends in a natural way the equational system for probabilistic bisimilarity given by Stark and Smolka by introducing an axiom for dealing with the Kantorovich distance between probability distributions.

KW - Markov chains

KW - Behavioral Distances

KW - Axiomatization

U2 - 10.4230/LIPIcs.CONCUR.2016.21

DO - 10.4230/LIPIcs.CONCUR.2016.21

M3 - Article in proceeding

SN - 978-3-95977-017-0

T3 - Leibniz International Proceedings in Informatics

SP - 21:1--21:14

BT - 27th International Conference on Concurrency Theory (CONCUR 2016)

PB - Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH

ER -

Bacci G, Bacci G, Larsen KG, Mardare RI. Complete Axiomatization for the Bisimilarity Distance on Markov Chains. In 27th International Conference on Concurrency Theory (CONCUR 2016). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH. 2016. p. 21:1--21:14. (Leibniz International Proceedings in Informatics, Vol. 59). https://doi.org/10.4230/LIPIcs.CONCUR.2016.21